A tilting micro-mirror is a central element in many MEMS or MOEMS devices. When used for scanning, its elements and operation principle ale shown in FIG. 1. A tilting micro-mirror (or simply “mirror”) 100 comprises a generally flat plate (e.g. made of silicon) that has a reflecting surface 104. Plate 102 is held suspended by two torsional hinges 106′ and 106″ aligned along a common torsion (and tilt) axis 108. The two hinges render mirror 100 operative to tilt clockwise and counterclockwise around axis 108 in a given range of angles (typically ±5 degrees). A laser beam 110 that impinges on the reflecting surface of the mirror is redirected by the mirror to a scanned area 112. The tilting mirror is actuated by an actuation moment 120 that can be provided by well-known MEMS actuation systems.
FIG. 2 shows the required time dependence of the rotational (or “tilt”) angle of a scanning mirror, i.e. the required shapes of a scanning path 202 to be followed by the reflected laser beam on scanned area 112. A triangular signal is needed for the forward-backward scanning, as shown in box 206, while a sawtooth signal 208 is needed for one directional scanning, as shown in box 210. 1>2>3>4>5>6 represent scans in the time domain. In this kind of applications, the necessity to create an image free of spatial and temporal distortions imposes specific requirements on the scanning micro-mirror motion. These include long term frequency stability and constant angular velocity (for small rotations), see J. H. Lee et al., Sensors and Actuators A-Physical 96 (2-3) pp. 223-230, 2002. A mirror of this type has been implemented recently in a virtual retinal display, see T. M. Lippert et al., “Overview of Light Beam Scanning Technology for Automotive Projection Displays”, available at Microvision Inc.® http://www.mvis.com/pdfs/sid_auto.pdf.
Tilt mirrors are also used in optical switches and variable optical attenuators implemented in communication systems, and in light processing devices used in projection technology, A large variety of designs and operational modes have been reported, depending on the requirements imposed by the specific application. For example, in optical communication applications, the requirements of long term positioning accuracy combined with high optical quality and low thermal sensitivity are the most challenging. In contrast, micro-mirrors used in projection devices for the digital processing of visible light must fulfill requirements of high reflectivity, short switching time and high reliability, while positioning issues are usually less crucial.
While linear motions are highly desirable in all micro-mirrors, it is difficult to provide it. The difficulty is mainly the consequence of the intrinsic nonlinearity and high level of uncertainty of operational forces developed by MEMS actuators. A large variety of micro-device actuation principles and methods are known. These include electrostatic, magnetic, thermal, piezo, laser and flow-induced actuation, as well as actuation based on shape memory alloys. Electrostatic actuation and magnetic actuation remain the most widely used methods. The main advantage of magnetic actuation is the linear relationship between the input signal (electric current) and the actuation force. However, the price paid is usually a high power consumption resulting in high heat generation, intricacy of the design and relatively complicated fabrication processes. In addition, the scaling laws of magnetic actuators are less favorable that those of electrostatic actuators.
The required typical size of a micro-mirror for scanning application in a retinal display (from hundreds of microns up to a millimeter) and the required operation frequencies (tens of KHz) make electrostatic actuation attractive for this use. In addition, advantages of electrostatic actuation include simple, well-established processes used for the fabrication of electrostatic devices, low power consumption, and developed modeling tools and large variety of design concepts reported in literature. However, the central difficulty of electrostatic actuation is the intrinsic nonlinearity of electrostatic forces. In the case of a scanning mirror, this results in a nonlinear dependence of the actuating torsion moment on the tilting angle and a nonlinear (quadratic) dependence on operational voltage. Moreover, the nonlinearity of electrostatic forces combined with the linearity of elastic restoring mechanical forces lead also to pull-in instability, which limits the operational range of the device.
To overcome these difficulties, different solutions were proposed in prior art. Specifically, a generated square root (of voltage) input signal was used by W Zhang et al., Applied Physics Letters 82(1) pp. 130-132, 2003, for the operation of a micro-resonator near the parametric resonance. The use of a vertical comb drive permits the elimination of the actuation moment dependence on the tilting angle and the reduction or even elimination of the square dependence on voltage, see e.g. J H Lee et al., Sensors and Actuators A-Physical 96 (2-3) pp. 223-230, 2002, H A Wada et al., Jpn. J. Appl. Phys. 41 (10B) pp. 1169-1171, 2002, and H Schenk et al., Sensors and Actuators A-Physical 89 (1-2) pp. 104-111, 2001. The necessity to provide a triangular signal which is required for video applications leads to very high actuation voltages or, in the case of magnetic actuation, very large currents. This difficulty is not related to the linearity of the motion and it is a result of high angular accelerations during the inversion of the velocity. To overcome this difficulty, frequency, I. Bucher, in Proc. of 29th Israel Conference on Mechanical Engineering, May 12-13, 2003, Technion, Haifa, Israel, suggested to represent the required triangular response as a Fourier series of sinusoidal components, and to excite each of these components at the resonance
The problems with tall such solutions include high complexity, difficulty to provide resonant frequencies with high accuracy, and consequently high sensitivity to fabrication tolerances and extreme difficulty in tuning the resonant frequency.
There is therefore a widely recognized need for, and it would be highly advantageous to have a scanning micro-mirror that has optimized motion linearity combined with high operational frequency and low actuation voltages.